Over a very long period of time, it has been noted that on Friday's 25% of the customers

at the drive-in window at the bank make deposits. What is the probability that it takes 4

customers at the drive-in window before the first one makes a deposit.

2. It is estimated that 45% of people in Fast-Food restaurants order a diet drink with their

lunch. Find the probability that the fourth person orders a diet drink. Also find the

probability that the first diet drinker of th e day occurs before the 5th person.

3. What is the probability of rolling a sum of seven in fewer than three rolls of a pair of

dice? Hint (The random variable, X, is the number of rolls before a sum of 7.)

4. In New York City at rush hour, the chance that a taxicab passes someone and is

available is 15%. a) How many cabs can you expect to pass you for you to find one that

is free and b) what is the probability that more than 10 cabs pass you before you find

one that is free.

5. An urn contains N white and M black balls. Balls are randomly selected, one at a time,

until a black ball is obtained. If we assume that each selected ball is replaced before the

next one is drawn, what is;

a) the probability that exactly n draws are needed?

b) the probability that at least k draws are needed?

c) the expected value and Variance of the number of balls drawn?

6. In a gambling game a player tosses a coin until a head appears. He then receives $2n ,

where n is the number of tosses.

a) What is the probability that the player receives $8.00 in one play of the game?

b) If the player must pay $5.00 to play, what is the win/loss per game?

7. An oil prospector will drill a succession of holes in a given area to find a productive

well. The probability of success is 0.2.

a) What is the probability that the 3rd hole drilled is the first to yield a productive well?

b) If the prospector can afford to drill at most 10 well, what is the probability that he will

fail to find a productive well?

8. A well-travelled highway has itstraffic lights green for 82% of the time. If a person

travelling the road goes through 8 traffic intersections, complete the chart to find a) the

probability that the first red light occur on the nth traffic light and b) the cumulative

probability that the person will hit the red light on or before the nth traffic light.

9. An oil prospector will drill a succession of holes in a given area to find a productive

well. The probability of success is 0.2.

a) What is the probability that the 3rd hole drilled is the first to yield a productive well?

b) If the prospector can afford to drill at most 10 well, what is the probability that he will

fail to find a productive well?

1. Calculate the Poisson distribution whose ? (Average Rate of Success)) is 3 & X (Poisson

Random Variable) is 6.

2. Customers arrive at a checkout counter according to a Poisson distribution at an average

of 7 per hour. During a given hour, what are the probabilities that

a) No more than 3 customers arrive?

b) At least 2 customers arrive?

c) Exactly 5 customers arrive?

3. Manufacturer of television set knows that on an average 5% of their product is defective.

They sells television sets in consignment of 100 and guarantees that not more than 2 set

will be defective. What is the probability that the TV set will fail to meet the guaranteed

quality?

4. It is known from the past experience that in a certain plant there are on the average of 4

industrial accidents per month. Find the probability that in a given year will be less that 3

accidents.

5. Suppose that the change of an individual coal miner being killed in a mining accident

during a year is 1.1499. Use the Poisson distribution to calculate the probability that in

the mine employing 350 miners- there will be at least one accident in a year.

6. The number of road construction projects that take place at any one time in a certain city

follows a Poisson distribution with a mean of 3. Find the probability that exactly five road

construction projects are currently taking place in this city. (0.100819)

7. The number of road construction projects that take place at any one time in a certain city

follows a Poisson distribution with a mean of 7. Find the probability that more than four

road construction projects are currently taking place in the city. (0.827008)

2. Each day is sunny, cloudy, or rainy. If it is sunny one day, there is a 50% chance that it will be sunny the following day and a 50% chance it will be cloudy. If it is cloudy one day, there is an equal 1 chance of = . 100% that it will be sunny, cloudy, or rainy the following day. If it is rainy one day, there is a 50% chance that it will be cloudy the following day and a 50% chance of rain. (a) Set up a stochastic matrix corresponding to this Markov process. Is the matrix regular? (b) Formulate a system of linear equations for finding the stable distribution for the process. (c) Use the Gauss-Jordan elimination method to solve the system of equations in (b).5. (10 pts) True of False: a) Gauss-Jordan elimination is the only way that you have learned in this class to invert matrixes: b) For a given vector space, there exist many possible inner products: c) If you calculate the eigenvalues of a 5x5 invertible matrix, you could end up with 3 unique eigenvalues and a total of 3 independent eigenvectors : . d) Given two square matrixes, A and B, having the same dimensions, AB and BA are not generally equal: e) If der (4)=0 , it is still possible for Ax=b to have a solution: f) If A is an 10x10 matrix and you determine that its nullity is 8, then you know that its rank must be 2: g) Cramer's Rule relies on Gauss Elimination to solve systems of linear equations: h) If I swap two rows in a matrix, it's determinant will changed: i) In the Markov Process problem, we use eigenvalue analysis to determine the final state of the system: j) 21=-1 could be an eigenvalue of an orthogonal matrix AQ1 (10 points) The owner of an online sports store wants to compare the sales with the geographical distribution of the population According to Statistics Canada (2006 Census), 7.2% of the population lives in the Maritimes, 23.9% in Quebec, 38.6% in Ontario, 17.2% in the Prairies and 13.1% in British Columbia. Here is the breakdown in a random sample of orders. Maritimes Quebec Ontario Prairies British Columbia 22 105 185 66 36 At the 1% level of significance, is the distribution of destination of the orders shipped reflective of that of the population? + Drag and drop your images or click to browse. Q2 (10 points) randomized to receive different dosages a+ 35% @10:24 PM Q2 (10 points) A drug study typically includes clinical trials whereby participants are randomized to receive different dosages as well as a placebo. Consider the following data with respect to gender and dosages. Gender 10-mg drug 20-mg drug Placebo Female Male N Test whether the drug is related to the gender. Use a = 0.01 + Drag and drop your images or click to browse